Question

Can someone please explain why sin2x = sqrt 2/2 has angles of pi/4, 3pi/4, 9pi/4, 11pi/4? I don't understand where the 9pi and 11 pi are coming from.

Answer 1

well there seems to be a slight mistake

if

\[\sin(2x) = \frac{\sqrt{2}}{2} ~~~~then~~~~~ 2x = \frac{\pi}{4}~~~or~~~ x = \frac{\pi}{8}\]

Answer 2

what if I gave you a different example?

Answer 3

but basically its because the curve repeats... based on the information it repeats over a distance of pi.... so the period is pi..


draw the cruve

draw a horizontal line through y = srt(2)/2 and you'll see how many times the horizonal line intersects sin(2x)

and it forms a pattern....

a rough sketch is shown below




hope it helps